Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...

http://dx.doi.org/10.1016/j.icarus.2014.03.013 0019-1035/ 2014 Elsevier Inc. All rights reserved. ⇑ Corresponding author. E-mail address: [email protected] (K. Krohn). K. Krohn a,⇑, R. Jaumann , K. Otto , T. Hoogenboom , R. Wagner , D.L. Buczkowski , B. Garry , D.A. Williams , R.A. Yingst , J. Scully , M.C. De Sanctis , T. Kneissl , N. Schmedemann , E. Kersten , K. Stephan , K.-D. Matz , C.M....

The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are related to cascade connections of automata of the first type. The introduced automata play a significant role in group theory and, hopefully, in the theory o...

objective: the present study was conducted to compare the effectiveness of two therapeutic approaches, namely, cognitive behavioral therapy (cbt) and stages of change model (soc) on improving abstinence self-efficacy in adolescent addicts. methods: forty five self-referred adolescent addicts were randomly selected to take part in this study. initial assessment was made using the following quest...

Dieter Fensel, Frank van Harmelen, Michel Klein, Hans Akkermans Free University Amsterdam VUA, Division of Mathematics and Informatics De Boelelaan 1081a, NL-1081 HV Amsterdam, The Netherlands http://www.ontoknowledge.org ; contact: [email protected] and Jeen Broekstra, Christiaan Fluit, Jos van der Meer, AIdministrator, The Netherlands Hans-Peter Schnurr, Rudi Studer, AIFB, University of Karlsru...

We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x and xy = xyx. This result has several consequences. We first use it together with a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Next, we give an algebraic proof of a theorem of ...

The notion of recognition of a language by a finite semigroup can be generalized to recognition by finite groupoids, i.e. sets equipped with a binary operation ‘ · ’ which is not necessarily associative. It is well known that L can be recognized by a groupoid iff L is context-free. But it is also known that some subclasses of groupoids can only recognize regular languages. For example, loops re...

We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety R of all finite R-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute J-pointlike sets, where J denotes the pseudovariety o...

The title result is proved by a Murskii-type embedding. Results on some related questions are also obtained. For instance, it is shown that every finitely generated semigroup satisfying an identity ξ d = ξ2d is embeddable in a relatively free semigroup satisfying such an identity, generally with a larger d ; but that an uncountable semigroup may satisfy such an identity without being embeddable...